MASTER'S THESIS

Building a PCB Milling Machine

Benny Strömberg

Master of Science in Engineering TechnologyElectrical Engineering

Luleå University of TechnologyDepartment of Computer Science, Electrical and Space Engineering

Benny Strömberg April 2012

Thesis report

Building a PCB milling machine

Table of content

I. Introduction ................................................................................................................................... 1

II. What is a circuit milling machine? .............................................................................................. 2

1. Milling the board ......................................................................................................................... 3

2. Moving the board ........................................................................................................................ 3

a. Linear components ........................................................................................................ 3

b. Motors ........................................................................................................................... 4

c. Sensors .......................................................................................................................... 5

3. Interface ....................................................................................................................................... 5

a. User interface ................................................................................................................ 6

b. Microcontroller ............................................................................................................. 6

c. Power supply, optocouplers .......................................................................................... 6

III. Designing the machine .................................................................................................................. 7

1. Dimensioning of the mechanical parts ........................................................................................ 7

a. Choice of screw ............................................................................................................. 7

b. Selection of the ball screw ............................................................................................ 8

c. Choice of linear bearings .............................................................................................. 9

d. Forces while milling .................................................................................................... 10

2. Designing the frame .................................................................................................................. 11

3. Dimensioning electromechanical components and electronics ................................................. 11

a. Choice of motor........................................................................................................... 11

b. Controlling the motors ................................................................................................ 13

4. Interface programming .............................................................................................................. 15

a. The microcontroller ..................................................................................................... 15

b. Programming the microcontroller ............................................................................... 16

c. User interface on a PC ................................................................................................. 18

5. Control theory choices ............................................................................................................... 20

a. Coordinate system ....................................................................................................... 20

b. Regulating the motors ................................................................................................. 21

c. Design of the PID controller ....................................................................................... 21

IV. Results........................................................................................................................................... 24

1. Building the machine ................................................................................................................. 24

2. Testing the machine ................................................................................................................... 25

3. Evaluation and discussion ......................................................................................................... 26

- 1 -

I. Introduction

The goal of this project is to design and construct a PCB milling machine. The design part consists of

four steps: machine specifications, machine frame blue print, programming and electronics design.

After the types components were selected, the search for suppliers began. This was a time consuming

part of the work since parts would turn out to be too expensive or with too long delivery time. The

machine was built and tested, there is however some improvements to be made.

I would like to thank my supervisor Kalevi Hyyppä for guidance and I would like to thank Stork

Drives for supplying motors at reduced price.

- 2 -

II. What is a circuit milling machine?

PCB stands for Printed Circuit Board and is a card where electronic components are mounted. As seen

on Figure 1 below it looks like a board with small roads on.

Figure 1: PCB1

These roads, or tracks, make the connections between different electronic components. In the final

stages of electronic design it is common to produce a number of prototype cards. These cards will be

used to test the components, and to verify that the final product will meet specifications.

The cards are covered with a thin layer of copper on one or both sides. Since the finished PCB should

only have copper tracks, i.e. connection, between some specific electronic components, excessive

material must be removed.

There is a number of different ways of doing this. The two major ones are chemical and mechanical.

The chemical approach [1] is to use a card with a thin layer of light sensitive material covering the

copper layers. This positive photoresistant material degrades in ultraviolet light. The wanted pattern is

printed on a plastic sheet attached on the board, and exposed to ultraviolet light. The plastic sheet is

removed and the board is then placed in a chemical solution removing the copper material lying where

the light sensitive material has been degraded. The next step is to remove the light sensitive material

that has not been exposed to the ultraviolet light. Finally, holes are eventually drilled in the board.

The mechanical solution is to use for example a PCB milling machine. In this case, a metal tool

“mills” the copper to remove the excessive material. It can also be done with a laser. In both cases, the

tool is mounted on a frame with two motors and can move along x and y axis. The rotational

movement of each motor is converted to linear motion.

1 Source: http://www.elec-intro.com/printed-circuit-board-manufacturing

- 3 -

I will now go through the main components needed when building a circuit milling machine.

1. Milling the board

To be able to remove material from the board, the main tool is the rotating cutter. The rotating cutter

can be seen as a drill, capable of absorbing forces in the x y plane while operating. To draw specific

copper tracks the rotating cutter needs to be moved with high position precision in the x y plane. It

should also move up and down to be able to move the drill without milling.

The frame of the machine will mainly carry the rotating cutter, the board to be milled, and the linear

components allowing them to move relatively to each other. It should be sturdy and will be drawn in a

CAD program for manufacturing. Its design depends on the other components choices, so it can need

many redesign phases during the components selection process.

2. Moving the board

a. Linear components

The simplest - and cheapest – way to get a linear movement is to use a sliding screw: a threaded rod

with bolt. If the bolt is unable to rotate it will travel up and down when the threaded rod is rotated.

This solution is however very inefficient in converting the rotational movement because of the sliding

friction.

Since position precision is very important for this application, there must not be any play when the

rotational direction is changed, referred to as backlash. This problem can be eliminated in two

different ways: using two nuts with a force pulling them together or pushing them apart or, when using

a ball screw, oversized balls. Both ways increase the torque and wear of the components and are

referred as preload [2].

The ball screw

Figure 2: A ball screw2

A better alternative than the sliding screw, considering friction, is the ball screw. As it can be seen on

Figure 2 above, it is a screw with balls between the screw and the nut threads. This results in a rolling

friction instead of sliding friction. There are two kinds of ball screws, differing by their manufacturing

process: grinded or rolled. To grind a screw means that a small fixed metal tool creates the thread

while the initial cylinder is rotating forward.

2 Source: http://www.directindustry.com/prod/hiwin/ball-screws-14370-28821.html

- 4 -

An advantage with the grinding method is that some errors during manufacturing can be corrected.

The rolling process is very different, the initial cylinder is moving forward between two rotating dies,

or big threaded cylinders. The rolled process is much faster, but puts a lot of strain on the screw. It is

also less precise, and the errors created during manufacturing will still be there in the final product.

Linear bearings

A ball screw is only meant to drive a load forward and back. Consider a ball screw in an x y z plane,

placed so the screw is aligned with the x-axis and the nut can travel along the x-axis. The

specifications imply that the screw should not deal with any force from the y or z plane. If it was to

occur, the ball screw might get damaged. This means that additional mechanical components will be

needed to carry the load and absorb the unwanted forces.

There exist a wide range of components for this problem. One solution is a precision steel rod with

ball bearings guide rails.

Finally, the motor controlling the ball screw needs to be connected to it with a coupling. There are

many different ones, with some of them accepting small position alignment errors between the motor

and ball screw. This is a very interesting property for me since it means that the mounting does not

need to be perfect, and thus reducing the frame manufacturing tolerance. The Oldham coupling on the

Figure 3 below has this property.

Figure 3: Oldham coupling3

b. Motors

Three motors are needed: two to rotate the screws and one is also needed to move the rotating cutter

up and down, so that contact can be made with the material.

When it comes to the motors moving the ball screws, there are two main families to choose from:

either analog motor or step motor. The analog motor, for example a DC motor, rotates with a speed

depending of the power applied and the load. It is then necessary to use feedback to be able to know

the exact rotation speed and angle. In this case the accuracy is limited by the feedback sensor

resolution.

The step motor moves in steps, so it does not require feedback, which makes it easier to control. It is

however not as fast to react as an analog motor since the analog has higher torque. The step motor has

also a limited resolution because of the steps.

When the choice is made, a motor driver card will have to be bought or designed for the specific motor

type.

3Source:http://stepper3.com/index.php?main_page=product_info&products_id=148,http://www.ruland.com/a_pr

ess_releases_us607.asp

- 5 -

c. Sensors

Incremental encoder

If analog motors are selected, then the needed feedback can be given by an encoder. An example is the

incremental encoder [3] sending a set number of pulses per revolution. This sensor is usually an

optical one, and consists then of three parts: a light source, a disk with one or more rings of holes, and

a light detecting component, see Figure 4.

The disk is mounted on the motor shaft and creates pulses by regularly letting light through during the

rotation. The pulses are counted during a time interval and the speed can then be calculated. Since

there are two sets of rings with holes shifted by 90 degrees, it is also possible to deduce the rotational

direction.

Figure 4: Incremental encoder4

End position sensors

In case of a problem, like for example a communication loss or a faulty command, the machine might

“get lost” and try to move to a point outside the expected area. It is then necessary to use position

sensors to stop the motors when reaching the allowed boundaries. These consist of switches. These are

located on the maximum and minimum position on each axis.

3. Interface

We have now all the parts needed to mill the circuit, the next step is to be able to control the machine

from a computer. The Figure 5 below represents the different elements needed from the computer to

the machine.

4 Source: http://www.pc-control.co.uk/incremental_encoders.htm

- 6 -

Microcontroller

AT90USB1286

optocouplers

optocoupler

encoder X

XOR

H-bridge X motor X

servo

Power

supply

USB

H-bridge X H-bridge Y

power

pulses

to H-bridge Y

from encoder Y

control

5V

5V

5V

5V

5V

5V 5V

5V

5V

12V 12V

5V

Figure 5: Computer-machine interface

a. User interface

A graphical user interface in the computer should allow the user to send commands to the machine, for

example by drawing a circuit or giving a set of angle and distance commands. It should be intuitive

and easy to use, giving the possibility to quickly create a new circuit. However, developing a good

user interface is very time consuming so it will in this work be kept as basic as possible, the focus

being on building the machine.

b. Microcontroller

Since an average computer will not have enough ports to control everything, it is necessary to use an

external hardware as interface. This hardware should be able to control the motor drivers and receive

signals from the incremental encoders; the connection with the computer should be either RS232 or

USB.

This external hardware is called a microcontroller. It is programmable and can have specific internal

hardware, for example motor driver capabilities.

There are many different microcontroller brands with all different advantages: some offer very robust

free development platforms, while others have a wider range of controller, making it easier to find a

good match according to specifications.

c. Power supply, optocouplers

Finally, all the electronics and the motors need to get power to operate. Optocouplers were used to

separate the microcontroller, which is a low power unit, from the H-bridge, a high power unit. This is

done to prevent a failure in the H-bridge from reaching the microcontroller.

- 7 -

III. Designing the machine

There are many factors to consider when designing a machine, with two main constraints: the

economic part and the specifications part. The later may be changed to accommodate the first. With a

decided budget the specifications can be drafted. For a PCB milling machine the main factors are

precision and speed. Speed is important since it is a production tool.

Since I funded the project myself a lot of time was spent to find low-cost alternatives. Also, my

inexperience in designing machines made it difficult to get from the start a good estimate of the cost of

the different parts.

After estimating what could be achieved with my budget, I have set the following specifications:

- Work area: 200mm x 160mm

- Speed: 100mm/s

- Interface with PC: USB

The next step is to find suitable components to be able to meet the specifications. This appeared to be

a quite tedious and time consuming process, since promising components often turn out being too

expensive or not available because of a long delivery time.

I will now go through the selection process for the different parts of the machine.

1. Dimensioning of the mechanical parts

a. Choice of screw

As pointed before the application requires a high position precision, meaning that no backlash will be

tolerated. A preload must then be applied to the driving screw. The preload is responsible for making

sure that there is no delay when changing the rotational direction. The two different screws examined

for this application were the sliding screw and the ball screw. The sliding screw was however

excluded on an early base because of its many drawbacks, as seen in Table 1 below.

Ball Screw Sliding screw

Efficiency (not preloaded) 90-95% 32%

Fast feeding Low heat generation High heat generation

Preload solutions Common Not common

Price range > 400Eur < 60Eur

Table 1: Screw comparison [4]

Efficiency: The efficiency in this case is the ratio of energy that will be converted into a linear motion.

As it can be seen in the table below 90-95% of the rotational energy from motor will be converted into

linear motion for the ball screw. 5-10% of the energy becomes heat. The loss in both types of screw

depends on friction.

Fast feeding: Fast feeding [5] means when the screw is rotated with high speed. It is not possible with

a sliding screw with preloaded nut because the high friction would result in too high temperatures.

- 8 -

b. Selection of the ball screw

The selection process consists of choosing an existing ball screw, and checking that all different

specifications are fulfilled. The last thing to check is the availability and price, this is done last since

the company needs to be contacted by mail or phone. If one of these specifications is not met, then

another ball screw must be examined.

Input variables

The different variables used as input for the selection are as follow:

- Estimate of forces and friction involved, see Appendix 1 for calculations

- Movement specifications: speed, duty cycle

- Safety factor

- Ball screw properties

Depending on the operating conditions of the machine, the wear of the components differs. This has to

be taken into account when designing, to ensure that the machine will reach the desired lifespan and

that the screw will function as expected in the machine. This is the safety factor and can be decided

with the help of the following Table 2. It is here set to 1.5 since there will be small impacts when the

milling tool is lowered on the card.

Run type Factor

Impactless Run 1.0~1.2

Normal Run 1.2~1.5

Run with Impact 1.5~2.0

Table 2: Safety factor

Here are some properties characterizing a ball screw.

- Basic Load Rating: tells which size of load the screw can handle. When choosing a ball screw it is

important to be sure that it will be able to absorb the forces required by the application. This depends

of the diameter, length, and mounting of the screw. A screw with as bigger diameter can take higher

forces but has a higher inertia and may require a bigger motor.

- Lead: it is the distance the nut will travel when the screw is rotated one revolution. The lead is

selected considering travel speed of the nut and accuracy. If fast travel speed is needed then a ball

screw with a higher lead is selected. Using a ball screw with a small lead where high travel speed is

needed will increase the rotational speed. This will create more heat, and so it might affect the

accuracy negatively.

- Tolerance: it describes the mean travel error per given distance, and expressed with a C and a

number for the tolerance grade. By checking with the manufacturer in a datasheet, for example the

mean travel error for a ball screw with a C7 tolerance would be 52µm per 300m. A ball screw with

lower number will have a smaller error for the same travel length. But with smaller error comes a

higher price. Since the threaded length is known by the designer and the needed accuracy known by

specification, the needed ball screw tolerance can be found in the datasheet.

- Maximum rotational speed: Another important factor, this can be calculated with information from

the manufacturer (see Appendix 1 for calculations).

- 9 -

Check against the ball screw limitations

The calculations made in Appendix 1 give then the operating point of the system. It needs to be within

the chosen ball screw operating range (specifications).

A ball screw has many specifications; here are some of the most interesting ones:

- Dynamic load rating

- Maximal rotation speed

- Tolerance class

- Available preload

An important point is that the accuracy will depend of the use of the screw: the heat can get the screw

to expand, and that will affect the accuracy of the system. This makes it important to not have too

much preload. In some critical applications active cooling of the nut is applied to counter thermal

expansion.

The most optimum preload value is a third of maximum axial force according to THK which is a big

manufacturer of ball screws. For this PCB milling machine this would mean a preload of about 3N. A

too large preload would result in higher wear and heat generation. If the preload is too low it will not

prevent backlash and accuracy requirements will not be met. No ball screw with that low preload was

found. The selected one has a preload of about 56N.

Choice of manufacturer

I started by asking different Swedish companies for offers on suitable ball screws, but they turned out

to be too expensive and often with long delivery time. So I extended the search to worldwide and

eventually found the Misumi Company located in Japan. They have a wide selection of linear

components (screws and bearings) and their prices are directly in the catalog, thus no need to ask for

an offer. It is a big advantage to be able to order all the mechanical components from the same

company: I would only need to deal with one supplier and save money on shipping.

The ball screw model I selected was the BSX1205: a grinded ball screw with C3 tolerance. It meets

the specifications. The datasheet is in Appendix 2.

c. Choice of linear bearings

As described earlier, the ball screw can only absorb forces that are parallel with the screw, so

additional components are used. These components will guide the platforms and carry the load, so the

ball screw only needs to move the platforms forward and back. The best performance within budget

was to use precision steel shafts and linear ball bushings. The bushing is a hollow cylinder that travels

on a precision rod usually made of steel. The simplest busing is just a material with low friction that

glides on the rod. To reduce friction even more, it is possible to use bushings with balls, using rolling

friction instead of sliding.

There are also better components such as guide rails but they are more expensive.

- 10 -

When it comes to deciding the linear components, ease of mounting is a priority. The ball bushing I

selected comes mounted in a pillow block, see Figure 6. The advantage by selecting the bushings

already mounted is that it simplifies the frame manufacturing and mounting.

Figure 6: Bushing mounted in a pillow block5

The milling machine has two platforms, one for each axis, that need to be guided. Each platform is

guided by four bushings with pillow blocks. These four bushings travel in pairs on two precision steel

rods. In the middle of the platform the ball screw nut is attached. This configuration can be seen below

on Figure 7.

Figure 7: Screw with linear bushing

d. Forces while milling

During milling the strain increases on the linear components. However, since the application is only

removing a very thin layer to create a PCB card, no calculations were made to check the increased

forces.

This was not done because it was not possible in the given time and budget to find linear components

that were optimal. An optimal component has a safety factor between 1 and 2 depending on the

application. The components that are used in this project have safety factors much higher than 2.

5Source:http://uk.misumi-ec.com/eu/CategorySearchView/103_20000000_20040000_20040900_20040904.html

- 11 -

2. Designing the frame

All the linear components, the rotating cutter, and the circuit board, need now to be mounted on a

frame, rigid and sturdy. I chose a simple construction where the milling rotating cutter travels in one

direction and the work area with the circuit board moves in the other direction, see Figure 8.

Figure 8: Design of the frame

The rotating cutter is attached on a vertical platform traveling along the x-axis with help of linear

components fixed on a vertical board. In a similar way, the PCB card is attached to a horizontal

platform, the work table, moving along the y-axis with help of linear components fixed on a horizontal

board. Both boards are then attached to each other so that the rotating cutter ends up above the work

table.

Since the linear components need to be mounted with precision to simplify mounting and avoid

misalignments, it felt necessary to have it manufactured with a CNC (Computer Numerical Control)

machine. The initial design was modified twice to simplify the manufacturing process, and so reduce

the cost.

3. Dimensioning electromechanical components and electronics

a. Choice of motor

I chose to use analog motors, and more specifically the simplest analog motor type: the DC motor.

This motor has two connectors connected to the positive and negative poles of the DC supply. To

change the rotational direction the connectors are switched. The speed is affected by the voltage

supplied to the motor.

- 12 -

A DC motor [6] consists of a rotor with copper winding, a shaft attached to the winding, and a

permanent magnet creating a magnetic field. When a voltage is applied to the winding it creates

another magnetic field, interacting with the permanent magnet. The interaction between the two

magnetic fields creates the rotation.

There are two different types of DC motors with similar working principles but different efficiency.

They differ in the way they are constructed.

Iron core rotor

The most common type has an iron core rotor. The copper winding is supported by the iron core as

seen below on Figure 9.

Figure 9: Motor with an iron core rotor6

When using a DC motor for positioning the iron core has a big drawback: the core interacts with the

permanent magnet poles. The result is an extra torque, called a cogging torque, and a tendency to stop

at preferential positions. The mass of the iron core also increases the inertia.

Iron free rotor

The other type of DC motor has an iron free rotor. Its construction can be seen on the Figure 10 below.

Figure 10: Motor with an iron free rotor7

6 and

7 Source:

http://www.maxonmotor.com/medias/sys_master/8798978113566/maxonDCmotor_Handouts.pdf?mime=applic

ation%2Fpdf&realname=maxonDCmotor_Handouts.pdf

- 13 -

As seen on Figure 10, the permanent magnet is in the center and the winding is outside. Since there is

no iron core the winding has to be self-supported. With no iron core any position can be easily

controlled, and the motor inertia is much lower, increasing the acceleration performance. However, a

drawback is that the winding will heat up faster.

I was recommended to look at ironless rotor motors from Maxon Motor because of the advantages of

these motors. I contacted the distributer in Sweden, Stork Drives, and they offered me a reduced price

on motors RE40 148877 (Datasheet in Appendix 3) with encoders they had in stock. It is not optimum

for the milling machine but it works fine.

b. Controlling the motors

H-bridge

To be able to drive a motor in both directions additional hardware must be used, in this case an H-

bridge. It can be seen as four switches that can be turned on or off individually. Two switches are

placed on each side of the motor as seen on Figure 11 below. The top switches are connected to the

positive pole of the power supply and the lower ones to the negative.

Figure 11: Working principle of the H-Bridge

When T1 and T4 are enabled, the motor shaft turns in one direction, and with T2 and T3 it turns in the

other direction. Precaution must be taken to prevent the possibility of turning on T1 and T2 or T3 and

T4 at the same time. This would create a short circuit since the switches have a very low resistance

(below 0.05Ω), and the current does not go through the motors. It can then damage the circuit by

overheating the components and is referred as shoot through.

Transistors

The analog to a switch in electronics is a transistor; it is the main component of the H-bridge. The

transistor used in this project, a MOSFET [7], consists of three pins: the source, the drain and the gate,

the gate being the control pin. There are different types of transistors, and in the H bridge case the

interesting specifications are Rds(on), gate capacitance, maximum voltage and current between source

and drain.

- Rds(on) is the resistance in the transistor when it is closed. A high value means a high

power loss that will be turned into heat. So the transistor should have as low Rds(on)

value as possible.

- The gate capacitance controls the time it takes to fully turn on the transistor. With a

higher gate capacitance the transistor will require more charge transfer or power to

turn on.

- The maximum voltage and current between the source and drain must be chosen so

there is a safety margin.

12V

M

T2 T1

T3 T4

- 14 -

A transistor fitting these specifications is the N-MOSFET. It is available with very low Rds(on). The

drawback is that the voltage between gate and source needs to be about 10V for the N-MOS transistor

to be fully on. This poses no problem for the two transistors connected to the negative or ground

source. But for the two transistors connected to the positive supply, it means that a voltage higher than

the supply voltage is needed. A solution for this is to use a H-bridge driver IC containing electronics to

increase the voltage from the supply. It can then be brought to a level high enough to turn on the

transistors.

The N-MOSFET transistor selected is the STP55NF06L, with a Rds(on) of 0.014 Ω in this application.

When applying a voltage on the transistor gate an oscillation can occur, to reduce this I used gate

resistors of 100Ω.

Pulse Width Modulation

The value of the voltage sent to an analog DC motor controls the speed of the motor. With a low

voltage the motor rotates slowly and with a high voltage the motor rotates fast.

Since the transistors are working as switches, in this application, they are considered either on or off

(not completely true since they are analog components), creating pulses that can be used in a Pulse

Width Modulation [8] (PWM) to control the motor speed.

100%

Pulse width: 25%

Supplied voltage: 25%

Figure 12: Pulse Width Modulation

As seen on Figure 12, the PWM has two parameters: frequency and pulse width. The frequency (in

Hertz) sets the number of pulses per second, and the pulse width sets the length of the pulse. It is often

expressed in percentage of the time the signal is in high state compared to the total PWM duration.

It means that with a 50% PWM, an H-bridge that is controlled by this signal will supply the motor half

of the voltage connected to the bridge. It is a very power efficient method of controlling a motor, since

the losses in the transistor are very low (total power loss in the H bridge of 2.3%).

It can be useful to be able to choose the PWM frequency because, for example, the component

controlled with the PWM pulse may only work with a given frequency. A very simple model of a DC

motor is a resistor and an inductor in series. This means that the motor can be seen as a low pass filter,

blocking the high frequencies and letting through the low ones. The threshold is given by the value of

the resistor and inductor.

The high frequencies of the PWM signal correspond to the sharp edges of the pulse. Since the DC

motor blocks high frequencies, the current will be the average of the signal over time. So the PWM

frequency should be much higher than the crossover frequency to make sure that the current is filtered

properly.

The motors used in this project have a resistance of 1.16Ω and inductance of 0.329mH. Using the

equation 1 below gives that the motor will block frequencies above 561 Hz.

(1)

- 15 -

Flyback diodes

The load driven by this H-bridge is a motor, and the resistor-inductor model of the motor can be used

to predict some important problem. An inductor is indeed an electronic component that will resist the

change of current. If the voltage over the inductor disappears it will try to make the current flow and

that will results in a reverse voltage spike of thousands of Volts. To protect the circuit, diodes are

added over each transistor. These diodes, called flyback diode, will conduct when the transistors are

shut off, bypassing them. They have to be as fast as possible and with a low “on voltage” when the

diode conducts. A standard diode has an on voltage of 1V for this application. In this case I used

“Schottky diodes”: they are faster and have a lower on voltage, about 0.65V for this application.

The final H-bridge circuit consists of four transistors, flyback diodes, resistors, and capacitors. The

schematics for the electronics can be seen in Appendix 4.

4. Interface programming

a. The microcontroller

A microcontroller controls the milling machine. It is a small one-chip low powered computer that can

execute small programs. A number of input and output ports can be used for control of external

hardware, for example a motor driver card.

Microcontrollers are today used for many applications, for example in microwave ovens, elevators,

cars, toys etc. There exists a wide range of different configurations depending on the task. Some have

an interface allowing them to be connected together or to a personal computer.

Interrupt ability

One of the main features of a microcontroller is the interrupt ability of the microcontroller. This means

that a port can be setup so that the normal running program will be interrupted by an external event.

When the interrupt is activated, some critical code can be executed, for example counting pulses from

the motor encoders. Interrupts are very user friendly on a microcontroller. On a PC it would however

require a good knowledge within hardware and operative system, so the usual method is to check the

inputs at a regular basis, also called polling.

PWM channels

Another common feature in microcontrollers is PWM channels. The PWM variables in a

microcontroller are: the time base (length of the pulse), the duty cycle (percentage of the pulse at high

state), and the resolution (number of steps between completely off and on).

Timers

A timer is needed to be able to execute code on given time intervals. A timer can be set to generate

interrupts at given intervals. The function has stopwatches and counts clock cycles. Since the amount

of clock cycles per second is usually in the range of millions, there is the possibility of scaling down

the counting. This is done by letting the timer count up to for example 1024 clock cycles before

stepping the actual count value by 1.

- 16 -

Compiler, Programmer/debugger

To be able to develop a program for a microcontroller we need a compiler and programmer/debugger.

The compiler translates the written code into a language the microcontroller can understand. The

program is then sent to the microcontroller by the programmer/debugger.

Choice of microcontroller

Developing a program for the microcontroller consist of three stages. The first is the planning stage,

with decision of the needed specifications. This includes the number of ports, PWM channels and

timers, and which interface to use for external communication. This stage also includes an estimate of

the code to execute and the time needed to execute it. The second stage consists of writing modules of

code and debugging each part. Finally, all parts are combined.

I was recommended to look at ATMEL for a microcontroller since their software development

program is free and they offer a relatively cheap programmer/debugger (600sek). The development

program is moreover easy to use and has debugging features. This means that the microcontroller can

be run and paused from the software on a PC. When the microcontroller program is paused, it is

possible to see and change the value of the settings and the variables. There is also a breakpoint

feature, making the microcontroller stop at a certain point in the program.

Table 3 displays the needed specifications for my milling machine.

Feature Amount

Input ports with interrupt capability 2

Output ports 6

PWM channels 3

Timers 2

Microcontroller to PC interface USB

Table 3: Microcontroller specifications

The microcontroller is a chip that needs to be mounted on circuit board with additional components to

be able to operate. To save time, I chose to buy the development board Teensy++ 2.0 hosting the

AT90USB1286 microcontroller which satisfies my specifications.

b. Programming the microcontroller

The program is first drawn as a sketch representing the different functions of the project, and then the

programming can begin. Functions can be grouped together, for example all motor control functions

will be in the same file. To each isolated group corresponds to “ .c file” for the code and a header file,

for example a datastruct, if needed. A datastruct is a way of managing the variables used by the

functions. This is useful when functions in a file are used for two or more different tasks.

A good example is the PID regulator that adjusts the speed of the motors to the given desired value.

Since there are two axes on the machine, each driven by a motor, two PID regulators are needed, and

so two PID structs are created at the beginning of the main code. Another advantage is that the code

becomes easier to reuse in other projects.

- 17 -

The Microcontroller program consists of the main file and five other files with data structures:

- Main

Initializes the datastructs and the timer for USB message check. Enters an infinity loop.

- Motor control functions

Initializes the output and input ports and the PWM channels. Called when a change of control

voltage is needed.

- Servo control functions

Initializes the PWM channel for controlling the servo. Called when the mill should be lowered

or raised.

- Angle function

To save clock cycles, the speed for the motors is pre-calculated and stored in arrays for given

angle (see section 5.a for a more precise description). The angle function takes in the

command angle and returns the speed for each motor.

- PID function: Atmel example

I used an example of code for PID regulation found on Atmel’s home page.

- USB function: Teensy example

For USB communication, I downloaded code from the company providing the Teensy++ 2.0

card.

- 18 -

c. User interface on a PC

A PC is needed to be able to control the machine by sending command to the microcontroller. A

program on the PC allows the user to create commands and send them. I chose to write it in C#

because it provides a good USB support. The USB code is from an example found on internet. As

pointed out in the beginning of this report, the graphical interface was kept as simple as possible.

Figure 13: User interface

As seen on Figure 13 above, the interface consists of three areas. The first part, in the lower left

corner, allows the user to create commands of straight lines movements and to add them to the

command list. The two text boxes take in the angle and the distance, and the cross box decides if the

machine should mill or not while moving. The second area shows the command list as it is sent to the

microcontroller. Finally, the send button on the left side sends the command list to the microcontroller.

When the acknowledge message is received from the microcontroller, a green label appears. The start

button sends the message to start executing the command list.

Program flow

The program flow is represented on Figure 14 below. When the microcontroller is started it waits for

the USB to be initialized. It then waits for incoming commands from the PC user interface. Each

message between the PC running the interface program and the microcontroller consists of 64 data

words; with the first data word defining the content of the message. The content can either be

commands to be stored, a program start or an emergency stop.

Each command consists of 8 data words, so a maximum of 7 commands can be sent per message.

After the program is uploaded, it can be started by sending a message with a start command. When the

start command is received, the microcontroller begins to execute commands, and does so until the

command queue is empty.

- 19 -

Microcontroller side PC side

Start of the device

USB initialization

Wait for the microcontroller id

on the USB

Message

in buffer?

Send one milling data package

(63 commands)

USB

buffer Get milling data

Store in own

buffer ACK

received?

Send

”ready to receive”

Send command ”start milling”

Control the

motors

Then stop all

motors

USB id

received?

Start of the program

USB id

Check USB buffer

Wait for ACK

ACK All data

sent?

Data

or ”start milling”

yes

no

no

no

no

yes

yes

yes

”Send button”

pressed

no

yes

Data start

milling

no ”Start button”

pressed

yes

Figure 14: Communication flow

- 20 -

5. Control theory choices

a. Coordinate system

When it comes to control, the PCB milling machine can be seen as a plane defined by a Cartesian

coordinate system. The rotating cutter is then a point moving between different coordinates, with the

help of the two motors attached to the x and y axis.

The chosen way of controlling the movement of the rotating cutter is to use polar coordinates, with

angle and length. By thinking in angles the different speeds needed for each of the motors can be

derived from the unit circle. This is true since each angle on the unit circle corresponds to an x value

and an y value. To convert the angle to a vector L(x,y), the following two equations are used.

(2)

(3)

Since the microcontroller chosen for this project does not have a floating point unit, additional code

is required to make the calculations. This would take a lot of time to execute. There are other solutions

to this problem and one is to limit the amount of possible angles and use look up tables. Since the unit

circle is centered in the origin, it is only necessary to store vector values for angles between 0 and 90

degrees. By identifying in which quadrant the angle is the vector can then be multiplied with -1 if

necessary, see Figure 15 below.

Since the cosinus and sinus can be derived from each other using the equations below, it is only

necessary to store vectors corresponding to either sin or cos.

(4)

(5)

In this project the travelling angle is controlled by the ratio of the two motors speed, and the number of

angle values is limited to 91, from 0 to 90. To each motor corresponds an array with 91 elements,

returning the rotational speed for a given angle value.

Cos is positive

Sin is positive

Cos is negative

Sin is positive

Cos is negative

Sin is negative

Cos is positive

Sin is negative

0

90

270

180

Figure 15: Quadrants in the unit circle

- 21 -

The 91 elements of the two arrays Xmotor and Ymotor can be calculated with the equations below,

with going from 0 to 90.

The r value is the linear speed of the rotating cutter in the plane, a constant affecting the speed of the

motors. It is set when creating the arrays, and was kept low for the first tests of the machine. I wrote a

program to create the two Xmotor and Ymotor arrays of motor speed, and then the lists of motor

speeds were implemented in the microcontroller.

b. Regulating the motors

The motors need to run at a given speed. Since the mechanical load will vary depending if the tool is

milling or not, a motor speed controller is needed. The use of a controller makes sure that the motor

rotates at the given speed: the output value of the motor is monitored, and if it differs too much from

the set value the controller will adjust the motor input. The difference between the output and the input

is called the control error.

The block diagram on Figure 16 below shows the relationship between the motor, the controller, and

the signals.

Figure 16: Principle of the controller

There are many types of controllers, using proportional (P), integrative (I), and derivative (D) factors.

To get a better regulation it is possible to use a combination of those factors to create for example a

PID controller.

For this application the chosen controller was the PID [9]. The reason was to achieve a short rise and

settling time.

c. Design of the PID controller

Creating the controller consist of 2 steps. The first step is to create a model of the motor and the

controller and to make a first calculation of the factors or use a method to derive them. It is then

necessary to apply these factors in the machine and trim them if necessary to achieve the wanted

performance.

Controller

(P, I, D)

Motor with

load

output

Σ +

-

set input motor

input

control

error

- 22 -

Model of the motor

The first step is to make a model of the motor with the axis and work table as load. This model is then

used to calculate the parameters of the controller.

Figure 17 shows basic electrical and mechanical models for a motor with load:

J

ω Mb

Me

Figure 17: Motor model

The motor is attached to the ball screw by a rigid coupling with no backlash. Because of this only one

model was made, including both the motor and the ball screw inertia in the same transfer function.

To be able to make a transfer function of the DC motor the variables in Table 4 below are needed.

Moment of inertia motor and load 0.0000138 +0.00000615 J

Damping ratio total system (estimated) 0.00316 Nms b

Electromotive fore constant 60,3 mNm/A K

Electric resistance 1,16 Ω R

Electric inductance 0,329 mH L

Friction Mb

Torque Me

Angular velocity =

Angular position θ

Table 4: Motor specifications

The electrical model gives the balance equation below.

(6)

The e variable in the equation stands for the induced voltage. It can be written as which is the

electromotive force constant multiplied with the angular velocity. The voltage over the inductor can

be written as

. The equation then looks as below.

(7)

Using Laplace Transforms: (8)

v

- 23 -

The mechanical model gives the following equation:

(9)

The torque is the same as the electromotive force constant multiplied with the current . The

friction can be written as which is the damping ratio multiplied with the rotational speed.

(10)

Using Laplace Transforms: (11)

After some calculations using equations (8) and (11), the transfer function for the motor can be seen as

below.

(12)

Controller model

I chose the PID controller, with the following transfer function.

(

) (13)

The model of the motor and the PID controller was simulated in Scilab Xcos, and the Ziegler-Nichols

[10] tuning was applied. The following factors were found:

Kp = 2.5

Ti = 0.11 s

Td = 0.0412 s

These values were later implemented in the microcontroller, and some tuning was made for each axis.

Sampling time

When testing running with the regulator I noticed that the process itself was quite rigid: it was stable

with good performance over a wider area than my initial expectation. However, I noticed a problem

when making a 90 or 180 degrees turn: there was a small delay before the change of direction because

of the low sampling frequency (100Hz).

In this case, the sampling frequency decides how often the regulator is activated. When it is activated

the regulator checks how many pulses came from the motor since the last check. The amount of pulses

is then compared to the set point, the wanted speed. The sampling frequency was set low because of

the low amount of pulses per revolution coming from the encoder.

One revolution of the ball screw corresponds to a linear distance of 5mm; it also corresponds to 2000

pulses sent from the incremental encoder. After checking experimentally how many pulses nb_pulses

were received from the encoders during the delay, the error in travel can then be calculated as follow:

(

) (14)

- 24 -

The solution I implemented to reduce the delay was to reduce the speed just before an incoming turn

to allow the process to react fast enough. The error before the fix was about 22 pulses from the

incremental encoder, so 0,055mm, after implementing the speed reduction it went down to 4 pulses

which correspond to 0.01mm.

This delay problem could also be solved by using a different way of control or by choosing an encoder

with higher resolution. Using higher resolution on the encoders would enable higher sampling

frequency, but those encoders are much more expensive.

IV. Results

1. Building the machine

The first idea was to build the frame of aluminum, but it turned out not to be possible because of

budget restrictions. The frame was instead constructed out of a wood product: MDF, Medium Density

Fiberboard. The MDF board was cut out in a CNC machine and the machine was assembled with the

ball screws and the motors. The change of the frame material increased the weight of the machine.

Figure 18: PCB milling machine

- 25 -

On Figure 19 below it is possible to see the x-axis motor coupled to the screw through an Oldham

coupling. The end sensor for this side of the axis is also visible on the top.

Figure 19: PCB milling machine

2. Testing the machine

As a first try to command the machine, I attached a pen instead of the milling tool and drew the circuit

on a paper. This gave good results, with acceptable precision.

However, milling a board is not as easy. I used a low cost solution to attach the rotating cutter and the

servo, consisting of drawer guiding rails and springs. It does work to control the rotating cutter up and

down but the cutter is coming down too fast on the board, damaging and finally breaking the milling

tool. It is also hard to adjust the lower position of the milling tool to remove the right amount of

material from the board.

The result when milling a board can be seen on Figure 20.

Figure 20: PCB

- 26 -

3. Evaluation and discussion

The goal of this thesis was to test if I could apply the knowledge I gained during my education to

build, from scratch, some kind of “mechatronics machine”. The choice of a PCB milling machine was

made because it seemed like a good combination of mechanics, electronics, programming, and control.

It is also relatively affordable and not too big, and I plan to use it to mill PCBs for some future

projects.

I consider that this project has been successful; the machine is up and running, even if needing quite a

few improvements. It was however not as easy as I expected: the theory in itself was not a problem,

but it was when interacting with the “industry world” that it became complicated. The part I

underestimated the most was definitely the time needed to select suppliers, parts, and components.

Future work

I will not list here all the work that can be done to improve the machine, since there is so much that

can be done! However there are two main points interfering with the usability of the machine: the third

axis for the rotating cutter has to be replaced for a better solution, and the user interface should be

more user friendly. It will be changed so that it can convert files into instructions to be sent to the

microcontroller.

i

Appendix 1: Ball Screw calculations

Selected input data:

Known values for sizing

Misumi bsx1205

Tolerance C 3

Diameter d 12 mm

Small diameter d1 9,5 mm

Lead Ph 5 mm

DN value DN 70000

Preload Mpreload 56,5 N

length L1 385 mm

Ball center to center diameter dp 12,8 mm

Dynamic load value Ca 3,74 kN

Static load value C0a 4,9 kN

Ball screw inertia 0.00000615

Duration tc 0,75 s

Constant speed duration tk 0,25 s

Acceleration duration t1 0,25 s

Deceleration duration t2 0,25 s

Gravity constant g 9,82 N/kg

Worktable mass m1 1,3 kg

Work piece mass m2 0,050 kg

Nut motion range ls 315 mm

Friction in guidance f 4 N

Ball screw efficiency n 0,9

Friction linear ball bushing µ 0,0012

Max speed Vmax 0,1 m/s

Values for mounting options

The values below are manufacturer specific depending on the mounting.

Fixed-free Fixed-

supported

Fixed-free

n 0.25 2 4

1.2 10 19.9

3.4 15.1 21.9

λ 1.875 3.927 4.73

All the following calculations are for the ball screw moving along the x-axis. Similar calculations were

also made for the other ball screw.

ii

1. Estimate of the length of the ball screw The ball screw can be divided into two parts, the threaded part and the machined part. The threaded

length is calculated as the wanted stroke plus the length of the nut and an additional safety length. The

safety length is used to make sure that the nut never travels further than the thread since this may

result in a destroyed ball screw. In this case it is done using end sensors cutting power to the motors.

The machined part is where the ball screw will be mounted on the support bearings on the frame.

Illustration 1: Threaded and machined parts

Machined part length lb 70 mm

Total ball screw length l 385 mm

Ball screw length between fix points la 330 mm

Table 1: Data for length calculation

2. Maximum axis force during operation The acceleration is calculated first. With the acceleration, the estimated forces during acceleration,

constant speed and deceleration, are calculated according to equations 1 to 7. The results are in the

Table 2 below.

Acceleration:

(1)

Acceleration positive direction:

(2)

At constant speed positive direction:

(3)

Deceleration positive direction:

– (4)

Acceleration negative direction:

– – – (5)

iii

At constant speed negative direction:

– – (6)

Deceleration negative direction:

– (7)

Acceleration α 0,40 m/s2

Acceleration positive direction Fa1 4,6 N

At constant speeds positive direction Fa2 4,1 N

Deceleration positive direction Fa3 3,5 N

Acceleration negative direction Fa4 -4,6 N

At constant speeds negative direction Fa5 -4,1 N

Deceleration negative direction Fa6 -3,5 N

Highest axial force Fa max 4,6 N

Table 2: Calculation results

From Table 2 the highest force is known: Fa max = 4.6N

3. Load limitations of the ball screw Buckling load is affected by the mounting technic used to attach the ball screw. The driving end of the

ball screw, where the motor is attached, is fixed to the frame. The other side can be mounted in three

different ways: fixed, supported or free. Fixed mounting at both ends gives the highest buckling load

but has high demands on mounting. Supported mounting gives a good enough buckling load. So for

this project the ball screws will be mounted fixed on the driving end and supported on the other. The

small diameter, see dc on Illustration 2 below is used to calculate buckling load.

Illustration 2: diameter measurements of the ball screw.

Calculation of the buckling load (la defined in Table 1):

(8)

7479 N (9)

iv

4. Maximum rotational speed The highest rotational speed is affected by two factors: a limit selected by the manufacturer and the

ball screw natural frequency.

Ball screw natural frequency

If a ball screw is rotated at the natural frequency, vibrations can damage the components. To avoid

this, the rotational speed for the natural frequency is calculated. A safety margin of 0,8 is included in

the equation 10 to assure that this speed is never reached.

(10)

131726 rpm

Rotational limit:

The manufacturer’s rotational limit depends on the manufacturing process: grinded or rolled. This

value is divided with the small diameter.

5468 rpm (11)

5. Life Span To be able to calculate average life span, the average load must first be calculated. The average load is

calculated as the total load given a repetition. The preload must also be added. In this case the exact

preload is not given. The datasheet specifies a maximum and a minimum and for this calculation the

maximum is used since it gives the lower life span. The maximum preload value is 56,5N.

The travel length from the acceleration, constant speed and deceleration must be calculated. These

travel length can be calculated from equations 12 and 13. The value for the acceleration α is found in

Table 2.

(12)

(13)

Acceleration travel length is 12.5mm and 25mm at constant speed. Deceleration travel length is the

same as the acceleration travel length.

The average load in positive direction is calculated from equation (14), and for average load in

negative direction is calculated from (15). and .

√

(14)

√|

| | | |

|

(15)

The result for both equations (14) and (15) is 56,5N.

In equation 16 below, the life span of the ball screw is calculated. The average rotation per min is

set to 1200. The work factor is selected as 2. average load is 56,5N. is the basic dynamic

load rating 3740N.

(16)

Result of the calculation above gives a life span of 500000h.

v

6. Calculation of required torque The needed torque can be divided in three parts: first the torque for the external load, then the torque

caused by the preload, and at last the torque needed for acceleration. To be able to choose a suitable

motor the average torque is also calculated.

The torque needed to move the external load is calculated in equation 17 below. The value comes

from Table 2, and is the maximum axial load.

(17)

Torque required for the preload from the datasheet:

To calculate the torque needed for acceleration the equation below is used, is the angular

acceleration and the inertia of the ball screw with motor and worktable and work material.

(18)

In equation 19 below the inertia is calculated. The A variable is if gears are used but since it is not

used this variable will be set to 1. is the ball screws inertia and the motor inertia 0.0000138

. Since there are no gears the gear inertia is 0.

(

) (19)

.

Angular acceleration:

⁄ (20)

Finally equation 18 can be calculated:

The necessary torque during uniform motion is given by equation 21 below.

(21)

The necessary torque during accelerating motion is given by equation 22 below.

(22)

The necessary torque during decelerating motion is given by equation 23 below.

(23)

With the three torques known, the average torque can be calculated in equation 24 below. This value is

important, the select motor must have a maximum continuous torque higher than this to not over heat.

√

(24)

Appendix 2: Ball Screw BSX1205

Appendix 3: Maxon Motor

Appendix 4: Electronic schematics

Bibliography

[1] MG Chemicals: Instructions for the Basic Positive Prototyping Process.

http://www.mgchemicals.com/techsupport/proto_pos-inst.html

[2] THK Ball Screw General Catalog. Preload p.705.

http://www.thk.com/documents/uk_pdf/product/general/a/ee_A15.pdf

[3] Faulhaber Optical encoder.

http://www.faulhaber.com/uploadpk/EN_HEDL_DFF.pdf

[4] THK Ball Screw General Catalog. Efficiency p.682.

http://www.thk.com/documents/uk_pdf/product/general/a/ee_A15.pdf

[5] THK Ball Screw General Catalog. Fast feed p.688.

http://www.thk.com/documents/uk_pdf/product/general/a/ee_A15.pdf

[6] Maxon motors. MAXON DC MOTOR.

http://www.maxonmotor.com/medias/sys_master/8798978179102/maxonDCmotor_Notes.pdf?mime=

application%2Fpdf&realname=maxonDCmotor_Notes.pdf

[7] Sedra, A and Smith, K. (2004) Microelectronics circuits, Fifth edition. pp.235-359.

[8] ATMEL PWM

www.atmel.com/Images/doc2542.pdf

[9] Lennartson, B. (2006) Reglerteknikens grunder, Fjärde upplagan. p.326.

[10] Lennartson, B. (2006) Reglerteknikens grunder, Fjärde upplagan. p.342.